Question

Is $-x^{2}+y^{2}=25$ an equation for a circle? Explain.

Name: Problem 130, Chapter 10: Intermediate Algebra for College Students
Uploaded: 2020-03-25T03:25:16-08:00
Duration: 44 s
Channel: Linh Vu
Description: Is -x^2+y^2=25 an equation for a circle? Explain.

   Is $-x^{2}+y^{2}=25$ an equation for a circle? Explain.

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 10, Problem 130

Instant Answer

Solved by Expert Linh Vu

03/25/2020

Step 1

Step 1: Recall the standard equation of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Show more…

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Is $-x^{2}+y^{2}=25$ an equation for a circle? Explain.

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Key Concepts

Role of Coefficient Signs in Conic Sections

The signs and coefficients of the squared terms in an equation help determine the type of conic section represented. In the given equation, the x² term has a negative coefficient while the y² term has a positive coefficient, which is inconsistent with the standard form of a circle and suggests that the graph represents a different conic section, such as a hyperbola.

Standard Form of a Circle

A circle’s equation is typically given in the form (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. Both x² and y² terms must appear with the same positive coefficient, indicating that all points are equidistant from the center.

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